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Vertex-algebraic structure of principal subspaces of basic \(D_{4}^{(3)}\)-modules

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Abstract

We obtain a presentation of the principal subspace of the basic \(D_{4}^{(3)}\)-module. We use this presentation to construct exact sequences involving this principal subspace, and obtain a recursion satisfied by its multigraded dimension. Solving this recursion, we obtain the multigraded dimension of the principal subspace of the basic \(D_{4}^{(3)}\)-module.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Colorado College, Colorado Springs, CO, 80903, USA

    Michael Penn

  2. Department of Mathematics and Computer Science, Ursinus College, Collegeville, PA, 19426, USA

    Christopher Sadowski

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  1. Michael Penn
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  2. Christopher Sadowski
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Correspondence to Christopher Sadowski.

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Penn, M., Sadowski, C. Vertex-algebraic structure of principal subspaces of basic \(D_{4}^{(3)}\)-modules. Ramanujan J 43, 571–617 (2017). https://doi.org/10.1007/s11139-016-9806-0

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  • DOI: https://doi.org/10.1007/s11139-016-9806-0

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